Ultralow expansion glass

ABSTRACT

Silica-titania glasses with small temperature variations in coefficient of thermal expansion over a wide range of zero-crossover temperatures and methods for making the glasses. The method includes a cooling protocol with controlled anneals over two different temperature regimes. A higher temperature controlled anneal may occur over a temperature interval from 750° C.-950° C. or a sub-interval thereof. A lower temperature controlled anneal may occur over a temperature interval from 650° C.-875° C. or a sub-interval thereof. The controlled anneals permit independent control over CTE slope and Tzc of silica-titania glasses. The independent control provides CTE slope and Tzc values for silica-titania glasses of fixed composition over ranges heretofore possible only through variations in composition.

This application claims the benefit of priority under 35 U.S.C. §119 ofU.S. Provisional Application Ser. No. 61/877,422 filed on Sep. 13, 2013the content of which is relied upon and incorporated herein by referencein its entirety.

FIELD OF THE DISCLOSURE

This disclosure pertains to a glass having ultralow thermal expansion.More particularly, this disclosure relates to silica-titania glasseshaving a small variation in coefficient of thermal expansion over atemperature range around the zero crossover temperature. Mostparticularly, this disclosure relates to annealing methods that permitindependent control of the temperature slope and the zero crossovertemperature of the coefficient of thermal expansion of silica-titaniaglasses and to silica-titania glasses formed by the methods.

BACKGROUND OF THE DISCLOSURE

Mirror substrates used in projection optics systems of extremeultraviolet lithography (EUVL) scanners must meet stringent thermalexpansion requirements in order to maintain their original surface shape(known as “figure”) when subjected to temperature changes caused byexposure to high power illumination during normal operation of thescanner. A temperature independent figure is necessary to avoidthermally-induced distortions in the wavefront characteristics of EUVprojection optics. For this reason, the preferred material for EUVLmirror substrates is Ultra Low Expansion glass (ULE® Glass),manufactured by Corning Incorporated. Glass sold by Corning Inc. underthe glass code 7973 is specifically tuned for EUVL applications. CorningEUVL glasses are characterized with high degrees of precision andaccuracy to properly identify mirror substrates that are narrowlytargeted to specific applications.

A defining feature of ULE® Glass is the existence of a temperature closeto room temperature at which the coefficient of thermal expansion (CTE)is exactly equal to zero. This temperature is known as the crossovertemperature, the zero-crossover temperature, or temperature of zerocrossover of the glass and is denoted Tzc. Another important feature ofULE® glass for EUVL is that the slope of the temperature-dependent CTEcurve (CTE slope) is extremely small within a temperature range close toroom temperature that includes Tzc. The CTE slope of ULE® glass is inthe vicinity of 1×10⁻⁹/K² (or, equivalently, 1 ppb/K²). EUVL mirrorsubstrates having Tzc near the temperatures expected when the mirrorsubstrate is exposed to an EUV optical source experience minimal thermalexpansion during operation of the EUVL scanner and a small CTE slopeensures that the minimal thermal expansion is preserved if fluctuationsin EUVL processing conditions cause variations in the thermalenvironment of the mirror substrate.

As EUVL technology advances, it is expected that higher energy opticalsources will be employed to increase system productivity. Thesemiconductor industry is also expected to improve the efficiency ofchip manufacturing processes by adopting larger wafer sizes (e.g. 450mm), which increases duty cycle and thus the range of mirror temperaturevariations. The push to reduce feature size and increase device densitywill require scanners with higher numerical aperture (NA), whichtranslates into an increase in the size of mirror substrates used inEUVL scanners. As the size of mirror substrates increases, therequirements for uniformity of Tzc and CTE slope will becomeincreasingly stringent and more challenging to achieve. As EUV opticalsources become more powerful and operate at new wavelengths, it willalso be necessary to develop mirror substrates that maintain desirableTzc and CTE slope characteristics over a wider range of thermalenvironments.

In order to meet the needs of the EUVL industry, it is desirable todevelop glasses and manufacturing processes that enable control over Tzcand CTE slope. Control over Tzc and CTE slope can provide for systematicvariations in Tzc and CTE slope in glass samples extracted fromdifferent parts of a boule (or other large glass monolith) so that asingle boule can be used to provide all of the mirror substrates neededto accommodate the range of thermal environments experienced by EUVLmirrors at different positions within a typical EUVL scanner. Mirrorsubstrate manufacturing efficiency can be improved if multiplesubstrates can be extracted from each manufactured glass boule ormonolith and the Tzc or CTE slope of each mirror substrate can beadjusted to meet the specific requirements of different mirrorcomponents in an EUVL scanner.

The prior art teaches that control of the fictive temperature, Tf, ofULE® Glass can be used to tune Tzc within a narrow range whilesimultaneously reducing CTE slope. A shortcoming of the prior art,however, is that control of the single parameter Tf simultaneouslyvaries both Tzc and CTE slope. In the methods of the prior art, Tzc andCTE slope are coupled and cannot be independently tuned. As a result,the glass manufacturer has been forced to finely tune the glass formingprocess to yield a glass composition such that, once Tf is controlled toa certain value, both CTE slope and Tzc will be within the rangerequired by the target application. Mirror substrates produced by priorart methods are therefore usable only within a narrow range of operatingconditions within an EUVL scanner. To enlarge the range of operatingconditions using prior art processing methods, it is necessary toprepare multiple glass boules or monoliths that differ in glasscomposition. Relying on compositional variations to meet the needs ofEUVL technology is inconvenient, costly, and time consuming. There is aneed for new processing methods that permit independent control of Tzcand CTE slope for a given glass composition over a wide range of values.

SUMMARY

The present disclosure provides glass articles and methods for makingglass articles. The glass articles may include silica-titania glass of agiven composition and may exhibit Tzc and/or CTE slope values heretoforenot possible for the composition. In prior art silica-titania glasses, aclose correlation exists between Tzc and CTE slope for glasses of agiven composition such that the range of Tzc values for a given CTEslope value (or the range of CTE slope values for a given Tzc value) isnarrow. In order to operate outside of the narrow ranges of the priorart, it is necessary to modify the composition of the glass and toendure the added time, cost, and complexity associated with fabricatingmultiple boules. For silica-titania glasses of a given composition inaccordance with the present disclosure, Tzc and CTE slope are notclosely correlated and may be varied independently over a wide range toobtain glasses that feature new properties and suitability for anexpanded range of applications.

The methods of the present disclosure may include annealing asilica-titania glass article. The annealing may include controlledanneals over two or more temperature regimes. The two or moretemperature regimes may include a higher temperature regime and a lowertemperature regime. The higher and lower temperature regimes may beconsecutive. The higher temperature regime may include temperaturesabove 750° C., such as temperatures in the range from 750° C. to 950°C., and the lower temperature regime may include temperatures between650° C. and the lowest temperature of the higher temperature regime. Therate of cooling in the lower temperature regime may be faster than therate of cooling in the higher temperature regime. The method may furtherinclude cooling below the lowest temperature of the lower temperatureregime.

The methods of the present disclosure may transform an initial glassarticle to a finished glass article. The glass article may includetitania-silica glass. The titania-silica glass may have a titaniacontent in the range from 5 wt % to 12 wt %, or in the range from 7 wt %to 12 wt %, or in the range from 6 wt % to 10 wt %, or in the range from7.5 wt % to 9 wt %. Additionally, the titania-silica glass may typicallyinclude OH in the range from 700 ppm to 1000 ppm by weight, or in anamount of about 850 ppm. The present invention also applies to higher orlower OH-containing silica-titania glasses, for which the relevanttemperature ranges may need to be appropriately adjusted within thescope of the present invention. These adjustments are required due tothe effect of OH content on the structural relaxation properties of theglass. Lower OH content generally results in a slower relaxing glass,and will require temperature ranges to be adjusted to higher values.Inclusion of further dopants in the glass can have similar effects, andwill also require adjustments to temperature ranges and cooling rateswithout departing from the scope of the present invention.

The zero-crossover temperature of the finished glass article may differfrom the zero-crossover temperature of the initial glass article, whilethe CTE slope of the finished glass article may or may not differ fromthe CTE slope of the initial glass article. Alternatively, the CTE slopeof the finished glass article may differ from the CTE slope of theinitial glass article, while the zero-crossover temperature of thefinished glass article may or may not differ from the zero-crossovertemperature of the initial glass article. It is worthwhile to note thatCTE slope depends on temperature. For the sake of clarity andconsistency, we will refer to the CTE slope at a fixed temperature of20° C. and we will denote this quantity by α′ or just “CTE slope”. Thisdoes not restrict the scope of the invention, as any other convenienttemperature could be chosen as a basis for comparison of the CTE slope.As EUV light sources become brighter and temperatures within EUVLscanners move to higher values, it may become convenient to choose ahigher temperature as a reference for measuring changes in CTE slope,without departing from the spirit of the present invention.

The zero-crossover temperature of the finished glass article may differfrom the zero-crossover temperature of the initial glass article by atleast 2° C., or at least 5° C., or at least 8° C., or at least 12° C.,or at least 16° C., or at least 20° C.

The CTE slope of the finished glass article may differ from the CTEslope of the initial glass article by at least 0.05 ppb/K², or at least0.10 ppb/K², or at least 0.15 ppb/K², or at least 0.20 ppb/K², or atleast 0.25 ppb/K².

The zero-crossover temperature of the finished glass article may differfrom the zero-crossover temperature of the initial glass article by atleast 2° C., or at least 5° C., or at least 8° C., or at least 12° C.,or at least 16° C., or at least 20° C. and the CTE slope of the finishedglass article may differ from the CTE slope of the initial glass articleby less than 0.10 ppb/K², or less than 0.07 ppb/K², or less than 0.05ppb/K², or less than 0.03 ppb/K².

The CTE slope of the finished glass article may differ from the CTEslope of the initial glass article by at least 0.05 ppb/K², or at least0.10 ppb/K², or at least 0.15 ppb/K², or at least 0.20 ppb/K² and thezero-crossover temperature of the finished glass article may differ fromthe initial zero-crossover temperature by less than 20° C., or less than15° C., or less than 10° C., or less than 5° C., or less than 3° C., orless than 1° C.

Among the methods of the present disclosure is:

A method of annealing glass comprising:

providing a silica-titania glass article, said silica-titania glassarticle having a first Tzc and a first CTE slope at 20° C.;

heating said glass article to a first temperature, said firsttemperature being in the range from 875° C. to 975° C.;

cooling said glass article at a first rate from said first temperatureto a second temperature, said second temperature being in the range from750° C. to 875° C.;

cooling said glass article at a second rate from said second temperatureto a third temperature, said second rate exceeding said first rate, saidthird temperature being in the range from 650° C. to 775° C.; and

cooling said glass article at a third rate below said third temperature,said third rate exceeding said second rate, said cooling at said thirdrate producing a finished silica-titania glass article, said finishedsilica-titania glass article having a second Tzc and a second CTE slopeat 20° C., said second Tzc differing from said first Tzc.

Among the methods of the present disclosure is:

A method of annealing glass comprising:

providing a silica-titania glass article, said silica-titania glassarticle having a first fictive temperature and a first Tzc;

heating said glass article to a first temperature, said firsttemperature being in the range from 60° C. below said first fictivetemperature to 10° C. below said first fictive temperature, said heatingexcluding exposing said glass article to a temperature greater than saidfirst fictive temperature;

cooling said glass article at a first rate from said first temperatureto a second temperature, said second temperature being at least 25° C.less than said first temperature;

cooling said glass article at a second rate to a third temperature, saidthird temperature being at least 50° C. less than said secondtemperature, said second rate exceeding said first rate, said coolingproducing a finished silica-titania glass article, said finishedsilica-titania glass article having a second fictive temperature and asecond Tzc, said second fictive temperature differing from said firstfictive temperature by less than 10° C., said second Tzc differing fromsaid first Tzc by at least 0.5° C.

The present disclosure extends to a silica-titania glass having atitania content between 7.45 wt % and less than 7.95 wt %, said glasshaving Tzc=25° C. and a CTE slope at 20° C. below 1.30 ppb/K². The glassmay include an OH concentration in the range from 700 ppm to 1000 ppm,or an OH concentration of about 850 ppm.

The present disclosure extends to a silica-titania glass having atitania content between 7.62 wt % and less than 8.13 wt %, said glasshaving Tzc=35° C. and a CTE slope at 20° C. below 1.30 ppb/K². The glassmay include an OH concentration in the range from 700 ppm to 1000 ppm,or an OH concentration of about 850 ppm.

The present disclosure extends to a silica-titania glass having atitania content between 7.56 wt % and less than 8.07 wt %, said glasshaving Tzc=25° C. and a CTE slope at 20° C. below 1.25 ppb/K². The glassmay include an OH concentration in the range from 700 ppm to 1000 ppm,or an OH concentration of about 850 ppm.

The present disclosure extends to a silica-titania glass having atitania content between 7.72 wt % and less than 8.23 wt %, said glasshaving Tzc=35° C. and a CTE slope at 20° C. below 1.25 ppb/K². The glassmay include an OH concentration in the range from 700 ppm to 1000 ppm,or an OH concentration of about 850 ppm.

The present disclosure extends to a silica-titania glass having atitania content in the range from 7.72 wt % to less than 8.03 wt %, saidglass having Tzc in the range from 25° C. to 35° C. and a CTE slope at20° C. of less than 1.30 ppb/K². The glass may include an OHconcentration in the range from 700 ppm to 1000 ppm, or an OHconcentration of about 850 ppm.

The present disclosure extends to a silica-titania glass having atitania content between 7.65 wt % and less than 7.95 wt %, said glasshaving Tzc=25° C. and a CTE slope at 20° C. below 1.30 ppb/K². The glassmay include an OH concentration in the range from 700 ppm to 1000 ppm,or an OH concentration of about 850 ppm.

The present disclosure extends to a silica-titania glass having atitania content between 7.82 wt % and less than 8.13 wt %, said glasshaving Tzc=35° C. and a CTE slope at 20° C. below 1.30 ppb/K². The glassmay include an OH concentration in the range from 700 ppm to 1000 ppm,or an OH concentration of about 850 ppm.

The present disclosure extends to a silica-titania glass having atitania content between 7.76 wt % and less than 8.07 wt %, said glasshaving Tzc=25° C. and a CTE slope at 20° C. below 1.25 ppb/K². The glassmay include an OH concentration in the range from 700 ppm to 1000 ppm,or an OH concentration of about 850 ppm.

The present disclosure extends to a silica-titania glass having atitania content between 7.92 wt % and less than 8.23 wt %, said glasshaving Tzc=35° C. and a CTE slope at 20° C. below 1.25 ppb/K². The glassmay include an OH concentration in the range from 700 ppm to 1000 ppm,or an OH concentration of about 850 ppm.

The present disclosure extends to a silica-titania glass having atitania content in the range from 7.92 wt % to less than 8.03 wt %, saidglass having Tzc in the range from 25° C. to 35° C. and a CTE slope at20° C. of less than 1.30 ppb/K². The glass may include an OHconcentration in the range from 700 ppm to 1000 ppm, or an OHconcentration of about 850 ppm.

The present disclosure extends to a silica-titania glass having atitania content in the range from 7.45 wt % to less than 8.23 wt %, saidglass having Tzc in the range from 25° C. to 35° C. and a CTE slope at20° C. of less than 1.30 ppb/K². The glass may include an OHconcentration in the range from 700 ppm to 1000 ppm, or an OHconcentration of about 850 ppm.

The present disclosure extends to a silica-titania glass having atitania content in the range from 7.45 wt % to less than 8.39 wt %, saidglass having Tzc in the range from 15° C. to 45° C. and a CTE slope at20° C. of less than 1.30 ppb/K². The glass may include an OHconcentration in the range from 700 ppm to 1000 ppm, or an OHconcentration of about 850 ppm.

Additional features and advantages will be set forth in the detaileddescription which follows, and in part will be readily apparent to thoseskilled in the art from the description or recognized by practicing theembodiments as described in the written description and claims hereof,as well as the appended drawings.

It is to be understood that both the foregoing general description andthe following detailed description are merely exemplary, and areintended to provide an overview or framework to understand the natureand character of the claims.

The accompanying drawings are included to provide a furtherunderstanding, and are incorporated in and constitute a part of thisspecification. The drawings are illustrative of selected aspects of thepresent disclosure, and together with the description serve to explainprinciples and operation of methods, products, and compositions embracedby the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts the coefficient of thermal expansion (expansivity) as afunction of temperature for three silica-titania glass compositions.

FIG. 2 depicts prior art annealing schedules used to adjust the fictivetemperature of silica-titania glasses.

FIG. 3 shows a relationship between zero-crossover temperature (Tzc) andCTE slope for silica-titania glasses subjected to prior art annealingschedules.

FIG. 4 compares correlated CTE slope and Tzc values available for aglass with a fixed composition from the annealing schedule of the priorart with uncorrelated CTE slope and Tzc values available from thepresent annealing schedules.

FIG. 5 compares correlated CTE slope and Tzc values available for aglass with a fixed composition from the annealing schedule of the priorart with uncorrelated CTE slope and Tzc values available from thepresent annealing schedules.

FIG. 6 shows representative annealing schedules that permit independentcontrol of Tzc and CTE slope.

FIG. 7 shows variations in Tzc and CTE slope for glass samples subjectedto annealing schedules in accordance with the present disclosure.

FIG. 8 shows alternative annealing schedules that permit independentcontrol of Tzc and CTE slope.

FIG. 9 shows annealing schedules of the type shown in FIG. 8 that wereemployed to test a series of six glass samples having a commoncomposition.

FIG. 10 shows Tzc and CTE slope data for glass samples treated with theannealing schedules of FIG. 9.

FIG. 11 shows CTE slope and fictive temperature data for glass samplestreated with the annealing schedules of FIG. 9.

DETAILED DESCRIPTION

The present disclosure provides a method of processing glasses thatprovides independent control over the zero-crossover temperature (Tzc)and temperature slope of the coefficient of thermal expansion (CTEslope) of glasses of a fixed composition. The present disclosure furtherprovides glasses produced by the methods.

The terms “article” or “glass article” shall be used herein to refer toan object or component made from glass. The glass article may be aboule, a blank, a sheet, a lump, or other glass configuration of anyphysical dimensions. The glass article may include titania-silica glass.The titania-silica glass may have a titania content in the range from 5wt % to 12 wt %, or in the range from 7 wt % to 12 wt %, or in the rangefrom 6 wt % to 10 wt %, or in the range from 7.5 wt % to 9 wt %. Theglass article may be formed directly by any method known in the art orit may be formed by consolidation of a glass preform made by any methodknown in the art. Silica-titania glass compositions are most commonlyused in EUVL systems and will be emphasized herein for purposes ofillustration. The methods of the present disclosure, however, are moregeneral and extend to glasses of any compositions, includingsilica-titania glasses containing OH, fluorine, chlorine or otherdopants.

The silica and titania precursors used to make a silica-titania glassmay be any silicon and titanium halide or organometallic compound knownin the art as useful for making such glass, or mixtures thereof. The CTEslope and Tzc of glass articles made from silica-titania glass may betuned using the methods described herein. ULE® glass by CorningIncorporated may be used herein, without limitation, as an exemplarysilica-titania glass and may be referred to herein as ULE glass orsilica-titania glass.

Representative methods of making silica-titania glass are described inU.S. Pat. Nos. 5,696,038, 5,970,751, 6,988,277, 7,155,936, RE 40586,7,410,922, and U.S. Patent Application Publication Nos. 2004/0027555,2007/0137252 and 2009/0143213, the disclosure of all of which areincorporated herein by reference. For example, U.S. Pat. No. 5,970,751describes a method and apparatus for preparing fused silica-titaniaglass. The apparatus includes a stationary cup or vessel. U.S. Pat. No.5,696,038 describes using oscillation/rotation patterns for improvingoff-axis homogeneity in fused silica boules using a prior art rotatingcup as described therein. U.S. Pat. No. 7,410,922 describes preparing asilica-titania glass by deposition of silica-titania particles on atarget such as a quartz rod or plate, and heating the depositedparticles to a vitrification temperature to obtain a silica-titaniaglass body. U.S. Patent Application Publication No. 2004/0027555describes a method for producing low expansion, titania-containingsilica glass bodies by depositing titania-containing glass soot andconsolidating it to form a silica-titania glass body, and furtherdescribes the lessening of striae by increasing the number of vents orexhaust ports of the furnace.

The semiconductor industry produces the silicon chips that have fueledthe information revolution that has occurred over the past few decades.The success of the semiconductor industry can be attributed tocontinuous improvements in the performance of semiconductor chips andcontinued reductions in manufacturing costs. Performance improvementsand cost reductions have been achieved primarily through miniaturizationof chips and devices and miniaturization has been made possible throughincreases in the optical resolution of lithography scanners. Sincelithographic feature size correlates with the wavelength of the opticalsource, there has been a strong demand to decrease the operatingwavelength of scanners in lithographic systems. The practical resolutionlimit achievable using traditional, refractive optics has been reachedat the current lithographic wavelength of ˜193 nm (ArF excimer lasers).Current ArF scanners are now reaching their minimum practical featuresize.

In order to decrease feature size and increase device density beyond thelimits of ArF scanners, the industry needs to find a new technology. Themost promising emerging technology is extreme ultraviolet lithography(EUVL). Several pilot-line EUVL tools are currently in operation andchip production using EUVL is expected to begin soon in the near future.A key difference between current, pilot-line and production-scale EUVLtools is the much higher light source intensity required for productionscale to fulfill throughput requirements. Future-generation EUVL toolsare likely to intensify the trend toward high intensity, high energy EUVlight sources to maximize manufacturing productivity and resolution.

EUVL is similar to current optical lithography in that it relies on anoptical projection system to reproduce features from a master reticle(also known as mask) onto a thin photosensitive layer (resist) depositedon the surface of a semiconductor wafer. EUVL operates at a wavelengthof ˜13.4 nm, a wavelength at which no known material is transparent.Thus, EUVL projection systems utilize reflective components (mirrors)rather than refractive elements (lenses). The extremely short wavelengthof the EUV radiation poses a number of challenges to the design of EUVLsystems. Reflective coatings on the mirrors, for example, arefundamentally limited to ˜70% efficiency, which means that ˜30% of EUVsource radiation is lost at each reflective surface in the scanner. Thelost radiation is absorbed as heat by the mirror substrate. Heatabsorption by the mirror substrate is undesirable because it may causethermal expansions or contractions of the substrate, which may deform oralter the reflective coating and lead to distortions in the wavefront ofthe reflected EUV radiation. Wavefront distortions, in turn, may lead todeterioration in the resolution of the EUVL system. Additionally, sincegases absorb 13.4 nm radiation, EUVL systems must operate under aninternal vacuum. Vacuum conditions make it more difficult to remove heatfrom the mirrors and exacerbate the problem of mirror heating.

Concerns over thermal effects associated with EUVL systems have promptedextremely tight requirements for the materials used to make the mirrorsubstrates. Silica-titania glass, such as ULE® glass, is presently thematerial of choice for mirror substrates in EUVL projection systems.ULE® glass has an extremely low coefficient of thermal expansion (CTE)at room temperature, which is critical in allowing the shape of themirror to remain substantially constant upon heating. ULE® glass alsofeatures low striae (which enables the production of very precise mirrorsurfaces), long term chemical and dimensional stability, andcompatibility with a vacuum environment.

Specifications for EUVL projection systems require Tzc of mirrorsubstrates to be within a very narrow range and to be highly uniformspatially. Precise control over the composition of silica-titania mirrorsubstrates is needed to achieve Tzc values within a narrow target range.In order to maintain spatial uniformity of Tzc, uniformity in thecomposition across the dimensions of the mirror substrates is needed.Spatial uniformity in composition will become increasingly challengingas the semiconductor industry continues the trend toward smaller featuresizes. Smaller feature sizes require mirrors with higher numericalaperture, which necessitates the use of larger mirrors. The need forlarger mirrors in EUVL projection systems requires compositionaluniformity over increasingly larger mirror substrates. In practice, itis becoming more difficult to reliably produce glass boules with theprecision and uniformity in composition over the larger areas needed tomeet the specification expected for EUVL mirror substrates.

It is further recognized that different mirrors in EUVL projectionsystems are subject to different thermal environments so that mirrorsubstrates having a range of Tzc values are needed to fully equip anEUVL system. In principle, a series of boules with differentcompositions could be used in the formation of mirror substratesspanning a range of Tzc values. FIG. 1, for example, illustrates thevariation of the coefficient of thermal expansion CTE (which may also bereferred to herein as “expansivity”) with temperature for threesilica-titania glasses. Trace 10 shows the variation for a glass articlehaving a standard glass composition (7.5 wt % titania and 92.5 wt %silica). Trace 12 shows the variation for a glass article havingcomposition B (>7.5 wt % titania and <92.5 wt % silica). Trace 14 showsthe variation for a glass article having composition A (<7.5 wt %titania and >92.5 wt % silica). Tzc corresponds to the temperature atwhich the expansivity is equal to zero (˜14° C. for composition A, ˜20°C. for the standard composition, and ˜26° C. for composition B).Although the data indicate that Tzc can be controlled by varying thetitania content of the glass, it is expensive and inconvenient inpractice to prepare multiple boules differing in titania content toachieve mirror substrates with different values of Tzc.

From a process efficiency standpoint, it is preferable to fabricate thefull set of mirror substrates needed for an EUVL system from boules ofthe same composition. It is more convenient to develop a standardizedmanufacturing process for producing boules of a single composition inhigh volume than it is to develop multiple processes for producingboules of varying composition. Boules of a fixed composition that areproduced in a high volume process can be screened after production forsuitability for a particular thermal environment within an EUVL systemand can be subjected to post-production annealing treatments to adjustproperties to optimize suitability for a particular application. Oncethe boule is optimized, it can be cut to produce multiple blanks havinguniform characteristics that are customized for a particularapplication. Different boules can be subjected to differentpost-production treatments to obtain blanks optimized for differentthermal environments within an EUVL system or different applications.Alternatively, blanks cut from a particular boule can be subjected todifferent annealing treatments to produce a series of mirror substratesfrom the same boule, each of which is optimized for a differentapplication. In order for a high volume manufacturing process based on asingle composition to succeed, post-production annealing processescapable of tuning the properties of the boule over a wide range must beavailable. As described more fully hereinbelow, the tunability availablefrom conventional annealing processes is limited and inadequate foradjusting boule characteristics over a range sufficient for practicalapplications. The present disclosure remedies this deficiency byproviding annealing processes that significantly enlarge the degree oftunability of boule properties.

In addition to Tzc, specifications for mirror substrates require atarget value of CTE slope and spatial uniformity of CTE slope across theglass article. CTE slope is a measure of the sensitivity of CTE withtemperature and is given by the tangent slope of data curves such as thetraces shown in FIG. 1. CTE slope may be defined more generally as therate of change of CTE with temperature. It is generally desired to havea small CTE slope.

The methods described herein may include cooling a glass article at aspecified rate from one temperature to a different temperature. As usedherein, the terms “cooling rate”, “rate of cooling”, “cooling at a rateof . . . ” and the like refer to an average cooling rate. The averagecooling rate may apply between two specified temperatures or below asingle specified temperature. As used herein, the term “CTE slope”refers to CTE slope at a temperature of 20° C.

In the fabrication of ULE® glass, the glass is formed in a hightemperature furnace and machined to form a boule or other glass article.The glass article is then subjected to a standard initial annealingprocess to relieve residual internal stresses and to promote spatialuniformity of glass properties. The conditions of the standard ULE®annealing process are:

ramping the temperature from 25° C. to 990° C. at a rate of 50° C./hour;

holding the temperature at 990° C. for 10 hours;

after the 10-hour hold, lowering the temperature from 990° C. to 850° C.at a rate of 3° C./hour; and

lowering the temperature from 850° C. to 25° C. at a rate of 25°C./hour.

The standard initial anneal establishes an initial fictive temperatureTf,0 and an initial CTE slope of the silica-titania glass that fallwithin narrow ranges. Greater variability, however, is observed in theinitial zero-crossover temperature Tzc,0 of the silica-titania glass dueto non-uniformities in spatial concentration of titania in the glass.The CTE slope of the silica-titania glass following the standard initialanneal is greater than the target value desired for EUVL mirrorsubstrates. To reduce CTE slope to the target range, the prior artdiscloses subjecting the silica-titania glass to a secondary annealafter completion of the standard initial anneal associated withconventional fabrication. The objective of the secondary anneal is toshift the fictive temperature of the silica-titania glass to atemperature low enough to obtain a CTE slope in the target range.

Typical temperature schedules disclosed in the prior art for thesecondary anneal are shown in FIG. 2. The glass article is heated to anelevated temperature, held at that temperature for several hours, cooledat slower rate to an intermediate temperature, and cooled from theintermediate temperature at a faster rate to a final temperature(usually room temperature). The elevated temperature is a temperatureabove the initial fictive temperature Tf,0 obtained in the standardinitial anneal. In FIG. 2, the elevated temperature is 950° C. Theintermediate temperature is a temperature below the minimum fictivetemperature achievable for the glass with annealing schedules withduration of up to a few weeks. The expectation in the prior art is thatcooling at the slower rate to temperatures much below the expectedminimum fictive temperature has only a minimal effect on the propertiesof the glass and serves only to unduly lengthen the process by delayingthe onset of the rapid cooling step. The intermediate temperature inFIG. 2 is 800° C. The rate of cooling from the elevated temperature tothe intermediate temperature is known in the art to determine thereduction in fictive temperature from the initial fictive temperatureTf,0. Faster cooling rates provide higher fictive temperatures thanslower cooling rates. The cooling rate from the elevated temperature tothe intermediate temperature is highest for annealing schedule 1 in FIG.2 and continually decreases over annealing schedules 2-6. A glassarticle subjected to annealing schedule 1 has a higher fictivetemperature than a glass article of the same composition subjected toannealing schedule 2, a glass article subjected to annealing schedule 2has a higher fictive temperature than a glass article subjected toannealing schedule 3 etc. After cooling to the intermediate temperature,the glass articles are subjected to a rapid cooling step. The rapidcooling step in the prior art annealing schedules occurs at a standardrate and variability in the prior art annealing schedules occurs only inthe rate of cooling between the elevated temperature and theintermediate temperature. In the prior art, the only considerationsgiven to the rate of cooling of the final rapid cooling step to roomtemperature is that it is quick enough to stop further evolution of Tf,and compatible with preserving the integrity of the glass body andequipment.

The variation in fictive temperature resulting from variation in therate of cooling between the elevated and intermediate temperatures inthe prior art secondary annealing process leads to variations in CTEslope and Tzc. FIG. 3 shows a calculated relationship between Tzc andCTE slope for a silica-titania glass having the approximate compositionby weight: 7.9% TiO₂, ˜92.0% SiO₂ and 850 ppm OH. Unless otherwisenoted, an OH content of ˜850 ppm is assumed in the examples discussedbelow. Each data point shown in FIG. 3 corresponds to the silica-titaniaglass after it had been subject to a secondary anneal of the prior artof the type shown in FIG. 2. The different data points correspond todifferent rates of cooling from the elevated temperature (950° C.) tothe intermediate temperature (800° C.). The other steps of the secondaryanneal were identical for each of the data points. Tzc and CTE slopewere computed for the annealing treatment corresponding to each datapoint for the glass composition. Both CTE slope and Tzc were observed toincrease as the cooling rate from the elevated temperature (950° C.) tothe intermediate temperature (800° C.) was increased. Data pointsaligned from left to right in FIG. 3 correspond to samples of thesilica-titania glass of fixed composition that were cooled atprogressively increasing rates from the elevated temperature (950° C.)to the intermediate temperature (800° C.).

The veracity of the calculation used to determine the data points shownin FIG. 3 was confirmed through measurements of selected points alongthe curve. Further confirmation was obtained through measurementsperformed on glass of different compositions. Glasses with differentcompositions have different initial Tzc values following the standardinitial anneal, but can be compared by plotting the change in Tzcinduced by secondary anneals of the prior art that utilize differentcooling rates as a function of CTE slope. The results of suchmeasurements provide a plot consistent with the trend shown in FIG. 3.

Although the data in FIG. 3 indicate that both Tzc and CTE slope can bevaried using the secondary annealing process of the prior art, it is notpossible to vary Tzc and CTE slope independently using the methods ofthe prior art. Instead, Tzc and CTE slope are correlated such that anyadjustment in fictive temperature resulting from cooling between theelevated and intermediate temperatures in the prior art predeterminesboth Tzc and CTE slope. A particular change in CTE slope, for example,is necessarily accompanied by a particular change in Tzc such that a 1:1correspondence between CTE slope and Tzc results from the prior artsecondary anneal. The data shown in FIG. 3 exemplify the correlationbetween CTE slope and Tzc.

Instead of correlated CTE slope and Tzc values for a glass of a givencomposition, it would be desirable to develop an annealing process thatpermits independent variation of CTE slope and Tzc. In the data shown inFIG. 3, for example, a silica(92.0 wt %)-titania(7.9 wt %) glasssuitable for an application requiring Tzc=50° C. necessarily has a CTEslope of about 1.57 ppb/K² at 20° C. This value of CTE slope may be toohigh for the intended application and may disqualify the glass fromconsideration. In order to achieve a low CTE slope, the correlation ofFIG. 3 indicates that a glass subject to a secondary anneal of the priorart necessarily has a low Tzc. With the prior art secondary anneal, aglass of a given composition having both a high Tzc and low CTE slope isnot possible.

The present disclosure provides a method of annealing glasses thatpermits independent control over Tzc and CTE slope. The presentdisclosure recognizes a deficiency in the prior art secondary annealingprocess. Specifically, the present disclosure recognizes that controlledcooling below the intermediate temperature of the prior art secondaryanneal influences the characteristics of the glass. The consistentintermediate temperature and consistent rapid cooling performed belowthe intermediate temperature in the prior art secondary anneal (as shownin FIG. 2) is believed to be responsible for the correlation of Tzc andCTE slope depicted in FIG. 3. By varying the intermediate temperatureand replacing the rapid cooling below the intermediate temperature witha slower, controlled cooling below the intermediate temperature to anannealing endpoint temperature that is well below the intermediatetemperature associated with the prior art secondary anneal, the presentdisclosure enables independent control of Tzc and CTE slope.

The method of the present disclosure includes subjecting a glass articleto an annealing protocol that includes controlled anneals over twodifferent temperature intervals. The glass article may be or include aglass that has previously been subjected to an initial anneal, such asthe standard initial anneal described hereinabove, during initialfabrication. The Tzc and CTE slope of the glass after fabrication andcompletion of the initial anneal may be referred to herein as theinitial Tzc (or Tzc,0) and the initial CTE slope (or α′,0),respectively. The glass may be a silica-titania glass. In the presentmethod, a first controlled anneal occurs over a higher temperatureinterval than a second controlled anneal. As described more fullyhereinbelow, the CTE slope of the glass article is determined primarilyby the higher temperature controlled anneal. Although Tzc of the glassarticle is primarily influenced by the higher temperature controlledanneal, it can be varied independently of CTE slope by the lowertemperature controlled anneal. Through control of the temperaturewindow, rate of cooling and annealing time of the higher and lowertemperature controlled anneals, the present method enables independentcontrol over CTE slope and Tzc to permit precise control over CTE slopeand Tzc over a wider range of values than is available from prior artannealing protocols.

The first controlled anneal occurs from an elevated temperature to anintermediate temperature. The elevated and intermediate temperatures maybe the same or different than the elevated and intermediate temperaturesdescribed hereinabove in connection with the secondary anneal of theprior art. The elevated temperature is a temperature near or above thefictive temperature of the glass article undergoing the controlledanneal. The first controlled anneal may adjust the fictive temperatureto a higher or lower temperature. For a silica-titania glass article,the elevated temperature may be a temperature of at least 850° C., or atleast 875° C., or at least 900° C., or at least 925° C., or at least950° C., or at least 975° C. or a temperature between 875° C. and 975°C., or a temperature between 900° C. and 950° C.

The intermediate temperature is a temperature less than the elevatedtemperature. The intermediate temperature may be less than or equal tothe ultimate fictive temperature of the glass article followingcompletion of the anneal of the present disclosure. For a silica-titaniaglass article, the intermediate temperature may be a temperature of atleast 750° C., or at least 775° C., or at least 800° C., or at least825° C., or at least 850° C. or at least 875° C., or a temperaturebetween 750° C. and 875° C., or a temperature between 775° C. and 875°C., or a temperature between 800° C. and 850° C.

The rate of cooling from the elevated temperature to the intermediatetemperature may be less than 10.0° C./hr, or less than 7.5° C./hr, orless than 5.0° C./hr, or less than 2.5° C./hr, or less than 1.0° C./hr,or less than 0.75° C./hr, or less than 0.5° C./hr, or less than 0.25°C./hr, or less than 0.10° C./hr, or between 0.01° C./hr and 10.0° C./hr,or between 0.01° C./hr and 5.0° C./hr, or between 0.10° C./hr and 7.5°C./hr, or between 0.10° C./hr and 5.0° C./hr or between 0.25° C./hr and5.0° C./hr, or between 0.50° C./hr and 5.0° C./hr.

The second controlled anneal occurs from the intermediate temperature toan annealing endpoint temperature. The annealing endpoint temperature isless than the intermediate temperature and greater than roomtemperature. The annealing endpoint temperature may be a temperature ofat least 650° C., or at least 675° C., or at least 700° C., or at least725° C., or at least 750° C. or at least 775° C., or a temperaturebetween 650° C. and 775° C., or a temperature between 675° C. and 775°C., or a temperature between 675° C. and 750° C., or a temperaturebetween 700° C. and 750° C., or a temperature between 675° C. and 725°C.

The rate of cooling from the intermediate temperature to the annealingendpoint temperature may be less than 300° C./hr, or less than 200°C./hr, or less than 100° C./hr, or less than 50° C./hr, or less than 25°C./hr, or less than 10° C./hr, or less than 5° C./hr, or less than 1°C./hr, or less than 0.5° C./hr, or less, or between 0.1° C./hr and 300°C./hr, or between 0.5° C./hr and 100° C./hr, or between 1.0° C./hr and50° C./hr, or between 2.0° C./hr and 25° C./hr, or between 2.0° C./hrand 20° C./hr, or between 2.0° C./hr and 15° C./hr, or between 2.0°C./hr and 10° C./hr.

After cooling to the annealing endpoint temperature, the glass articlemay be further cooled to a final temperature less than the annealingendpoint temperature to produce a finished glass article. The finaltemperature may be room temperature. The rate of cooling from theannealing endpoint temperature to the final temperature is arbitrary andmay be greater than the rate of cooling during the first controlledanneal and the rate of cooling during the second controlled anneal.

The examples presented hereinbelow demonstrate that controlled annealsover the higher and lower temperature windows of the present methodpermit independent control over Tzc and CTE slope. The conditions of thehigher temperature annealing process (e.g. elevated temperature,intermediate temperature and rate of cooling) are shown to have primaryinfluence over CTE slope, while the conditions of the lower temperatureannealing process (e.g. intermediate temperature, annealing endpointtemperature, and rate of cooling) are shown to have little effect on CTEslope. The conditions of the higher temperature annealing process alsoinfluence Tzc, but only in a way, as described hereinabove, that iscorrelated with the influence on CTE slope. The conditions of the lowertemperature annealing process, in contrast, permit control over Tzcindependent of CTE slope.

For a given CTE slope, utilization of the controlled anneals of thepresent disclosure permits tuning of Tzc for a silica-titania glass offixed composition over a much wider range than is possible with theprior art secondary anneal. Similarly, for a given Tzc, the presentmethod permits tuning of CTE slope for a silica-titania glass of fixedcomposition over a much wider range than is possible with the prior artsecondary anneal. The tunability in Tzc and CTE slope achievable withthe present methods has heretofore only been possible through variationsin glass composition. With the present methods, the need to prepareseparate boules of varying composition to achieve targeted Tzc and CTEslope values is avoided and a single boule of fixed composition may beemployed instead. Boules of a fixed composition may be prepared by astandardized process and subjected to controlled anneals of the presentdisclosure to provide boules spanning a wide range of Tzc and CTE slopevalues. Individual boules may be customized to applications requiringtargeted Tzc and CTE slope values, where the range of potential Tzc andCTE values is wide and the range of potential applications iscorrespondingly diverse. Alternatively, blanks extracted from a singleboule of uniform composition may be subjected to the controlled annealsof the present disclosure to provide glass articles having a range ofTzc and CTE slope values.

The methods of the present disclosure may transform a glass articlehaving an initial zero-crossover temperature (Tzc,0) and an initial CTEslope (α′,0) to a finished glass article having a final zero-crossovertemperature (Tzc,f) and a final CTE slope (α′,f). The zero-crossovertemperature of the finished glass article may differ from the initialzero-crossover temperature, while the CTE slope of the finished glassarticle may or may not differ from the initial CTE slope. Alternatively,the CTE slope of the finished glass article may differ from the initialCTE slope, while the zero-crossover temperature of the finished glassarticle may or may not differ from the initial zero-crossovertemperature.

The zero-crossover temperature of the finished glass article may differfrom the initial zero-crossover temperature by at least 2° C., or atleast 5° C., or at least 8° C., or at least 12° C., or at least 16° C.,or at least 20° C.

The CTE slope of the finished glass article may differ from the initialCTE slope by at least 0.05 ppb/K², or at least 0.10 ppb/K², or at least0.15 ppb/K², or at least 0.20 ppb/K², or at least 0.25 ppb/K².

The zero-crossover temperature of the finished glass article may differfrom the initial zero-crossover temperature by at least 2° C. and theCTE slope at 20° C. of the finished glass article may differ from theinitial CTE slope at 20° C. by less than 0.10 ppb/K², or less than 0.07ppb/K², or less than 0.05 ppb/K², or less than 0.03 ppb/K². Thezero-crossover temperature of the finished glass article may differ fromthe initial zero-crossover temperature by at least 5° C. and the CTEslope at 20° C. of the finished glass article may differ from theinitial CTE slope at 20° C. by less than 0.10 ppb/K², or less than 0.07ppb/K², or less than 0.05 ppb/K², or less than 0.03 ppb/K². Thezero-crossover temperature of the finished glass article may differ fromthe initial zero-crossover temperature by at least 8° C. and the CTEslope at 20° C. of the finished glass article may differ from theinitial CTE slope at 20° C. by less than 0.10 ppb/K², or less than 0.07ppb/K², or less than 0.05 ppb/K², or less than 0.03 ppb/K². Thezero-crossover temperature of the finished glass article may differ fromthe initial zero-crossover temperature by at least 12° C. and the CTEslope at 20° C. of the finished glass article may differ from theinitial CTE slope at 20° C. by less than 0.10 ppb/K², or less than 0.07ppb/K², or less than 0.05 ppb/K², or less than 0.03 ppb/K². Thezero-crossover temperature of the finished glass article may differ fromthe initial zero-crossover temperature by at least 16° C. and the CTEslope at 20° C. of the finished glass article may differ from theinitial CTE slope at 20° C. by less than 0.10 ppb/K², or less than 0.07ppb/K², or less than 0.05 ppb/K², or less than 0.03 ppb/K². Thezero-crossover temperature of the finished glass article may differ fromthe initial zero-crossover temperature by at least 20° C. and the CTEslope at 20° C. of the finished glass article may differ from theinitial CTE slope at 20° C. by less than 0.10 ppb/K², or less than 0.07ppb/K², or less than 0.05 ppb/K², or less than 0.03 ppb/K².

The CTE slope at 20° C. of the finished glass article may differ fromthe initial CTE slope at 20° C. by at least 0.05 ppb/K² and thezero-crossover temperature of the finished glass article may differ fromthe initial zero-crossover temperature by less than 5° C., or less than3° C., or less than 1° C. The CTE slope at 20° C. of the finished glassarticle may differ from the initial CTE slope at 20° C. by at least 0.10ppb/K² and the zero-crossover temperature of the finished glass articlemay differ from the initial zero-crossover temperature by less than 10°C., or less than 5° C., or less than 3° C. The CTE slope at 20° C. ofthe finished glass article may differ from the initial CTE slope at 20°C. by at least 0.15 ppb/K² and the zero-crossover temperature of thefinished glass article may differ from the initial zero-crossovertemperature by less than 15° C., or less than 10° C., or less than 5° C.The CTE slope at 20° C. of the finished glass article may differ fromthe initial CTE slope at 20° C. by at least 0.20 ppb/K² and thezero-crossover temperature of the finished glass article may differ fromthe initial zero-crossover temperature by less than 20° C., or less than15° C., or less than 10° C.

The ability to independently control CTE slope and Tzc means that thepresent annealing methods can vary CTE slope and Tzc in an uncorrelatedmanner. The range of variations in CTE slope and Tzc for a fixed glasscomposition is not constrained by a correlation such as the one shown inFIG. 3. Instead, variations of CTE slope and Tzc from initial values toarbitrary values is possible. Whereas prior art annealing schedulespermit transformations of CTE slope and Tzc among the different pointsalong a correlation such as the one shown in FIG. 3, the annealingschedules of the present disclosure permit transformations of CTE slopeand Tzc from a point on a prior art correlation such as the one shown inFIG. 3 to a point off of the prior art correlation, or from a point offof a prior art correlation to a point on a prior art correlation, orfrom one point off of a prior art correlation to a different point offof a prior art correlation.

FIG. 4 repeats the correlated Tzc and CTE slope values shown in FIG. 3and includes additional uncorrelated Tzc and CTE slope values for aglass having the same composition. As described hereinabove, thecorrelated Tzc and CTE slope values result from employing annealingschedules according to the prior art. Uncorrelated Tzc and CTE slopevalues refer to states described by points that do not lie on thecorrelation shown with the solid line. Uncorrelated Tzc and CTE slopevalues are available from the annealing schedules of the presentdisclosure. Point A shown in FIG. 4 represents a glass with Tzc and CTEslope values on the correlation. The glass represented by point A has aCTE slope of 1.57 ppb/K² and a Tzc of 50° C. If the application forwhich the glass is needed required a CTE slope of approximately 1.30ppb/K², annealing according to the prior art schedule would provide theglass represented by point B in FIG. 4. Because Tzc correlates with CTEslope, the glass necessarily would have a Tzc of 20° C. If a Tzc otherthan 20° C. were required for the application, the glass would beunsuitable.

Annealing according to the present methods permits transformation of theglass represented by point A to multiple states spanning a range of Tzcvalues for a target value of CTE slope. If a glass with a CTE slope of1.30 ppb/K² is desired, the present annealing methods can not onlyprovide the glass with Tzc=20° C. represented by point B available fromthe prior art annealing methods, but also glasses with Tzc values aboveor below 20° C. Glasses represented by points C, D, and E shown in FIG.4 schematically depict the tunability in Tzc available from methods ofthe present disclosure. The dotted lines illustrate transformations ofthe glass represented by point A to points C, D, E, and F and exemplifythe lack of correlation between CTE slope and Tzc using the methods ofthe present disclosure. Analogous tunability is available for glasseshaving any CTE slope value, including glasses having a CTE slope lessthan 1.70 ppb/K², or less than 1.60 ppb/K², or less than 1.50 ppb/K², orless than 1.40 ppb/K², or less than 1.30 ppb/K², or between 1.25 ppb/K²and 1.65 ppb/K².

FIG. 5 shows a similar schematic tunability in CTE slope available fromthe methods of the present disclosure. If a Tzc of 20° C. is desired fora glass represented by point A, the methods of the present disclosureare not limited to providing a glass with the correlated CTE sloperepresented by point B. Instead, methods of the present disclosure canprovide a glass with Tzc=20° C. with CTE slope values spanning a widerange, such as those illustrated by points F, G, and H in FIG. 5.Analogous tunability is available for glasses having any Tzc value,including glasses having a Tzc greater than 10° C., or greater than 20°C., or greater than 30° C., or greater than 40° C., or greater than 50°C., or between 10° C. and 50° C.

The glass may have a composition of 7.9 wt % TiO₂-92.0 wt % SiO₂ andconform to the correlation shown in FIG. 3. The initial state of theglass may have a CTE slope of 1.60 ppb/K² and a Tzc in accordance withthe correlation shown in FIG. 3 (˜52° C.) and the final state of theglass may have a CTE slope less than or equal to 1.30 ppb/K² and a Tzcof at least 22° C., or at or at least 24° C., or at least 26° C., or atleast 28° C., or at least 30° C.

The glass may have a composition of 7.9 wt % TiO₂-92.0 wt % SiO₂ andconform to the correlation shown in FIG. 3. The initial state of theglass may have a CTE slope of 1.60 ppb/K² and a Tzc in accordance withthe correlation shown in FIG. 3 (˜52° C.) and the final state of theglass may have a CTE slope less than or equal to 1.40 ppb/K² and a Tzcof at least 32° C., or at least 34° C., or at least 36° C., or at least38° C., or at least 40° C.

The glass may have a composition of 7.9 wt % TiO₂-92.0 wt % SiO₂ andconform to the correlation shown in FIG. 3. The initial state of theglass may have a CTE slope of 1.60 ppb/K² and a Tzc in accordance withthe correlation shown in FIG. 3 (˜52° C.) and the final state of theglass may have a CTE slope less than or equal to 1.50 ppb/K² and a Tzcof at least 42° C., or at least 44° C., or at least 46° C., or at least48° C., or at least 50° C.

The glass may have a composition of 7.9 wt % TiO₂-92.0 wt % SiO₂ andconform to the correlation shown in FIG. 3. The initial state of theglass may have a CTE slope of 1.60 ppb/K² and a Tzc in accordance withthe correlation shown in FIG. 3 (˜52° C.) and the final state of theglass may have a CTE slope greater than or equal to 1.25 ppb/K² and aTzc of or less than 14° C., or less than 12° C., or less than 10° C., orless than 8° C.

The glass may have a composition of 7.9 wt % TiO₂-92.0 wt % SiO₂ andconform to the correlation shown in FIG. 3. The initial state of theglass may have a CTE slope of 1.60 ppb/K² and a Tzc in accordance withthe correlation shown in FIG. 3 (˜52° C.) and the final state of theglass may have a CTE slope greater than or equal to 1.35 ppb/K² and aTzc of or less than 24° C., or less than 22° C., or less than 20° C., orless than 18° C.

The glass may have a composition of 7.9 wt % TiO₂-92.0 wt % SiO₂ andconform to the correlation shown in FIG. 3. The initial state of theglass may have a CTE slope of 1.60 ppb/K² and a Tzc in accordance withthe correlation shown in FIG. 3 (˜52° C.) and the final state of theglass may have a CTE slope greater than or equal to 1.45 ppb/K² and aTzc of or less than 36° C., or less than 34° C., or less than 32° C., orless than 30° C.

The glass may have a composition of 7.9 wt % TiO₂-92.0 wt % SiO₂ andconform to the correlation shown in FIG. 3. The initial state of theglass may have a CTE slope of 1.60 ppb/K² and a Tzc in accordance withthe correlation shown in FIG. 3 (˜52° C.) and the final state of theglass may have a CTE slope greater than or equal to 1.55 ppb/K² and aTzc of or less than 46° C., or less than 44° C., or less than 42° C., orless than 40° C.

As noted hereinabove, the correlation shown in FIG. 3 corresponds to aparticular titania-silica glass composition, including ˜850 ppm OH.Corresponding correlations exist for other titania-silica glasscompositions and are generally parallel to the correlation shown in FIG.3. Departures from such correlations analogous to those described hereinfor the correlation shown in FIG. 3 are within the scope of the presentmethods.

Although FIGS. 4 and 5 illustrate aspects of the present disclosure witha glass having an initial state represented by a point (point A) on thecorrelation of the prior art, the present methods are not so limited.The present methods may transform glasses having initial states not onthe correlation of the prior art to glasses having final statesrepresented by points either on or off of the correlation of the priorart. A glass having an initial state represented by point H of FIG. 5,for example, may be transformed to a final state represented by point Eof FIG. 4 (or vice versa). Transformations available from the presentannealing methods may thus induce changes in both Tzc and CTE slope ofthe glass such that the Tzc and CTE slope of the final state of theglass both differ appreciably from the Tzc and CTE slope of the initialstate of the glass. One or both of the differences between the final Tzcand initial Tzc and the final CTE slope and the initial CTE slope maydiffer from the corresponding difference represented by the correlationobtained from the annealing method of the prior art.

The prior art correlation shown in FIG. 3 is essentially linear with aslope of 107° C./(ppb/K²), where slope is defined as the ratio of thedifference between Tzc and the difference between CTE slope for twopoints on the correlation. Methods of the present disclosure providetunability such that the ratio of the difference between Tzc and thedifference between CTE slope for the initial and final states is greaterthan 107° C./(ppb/K²) (e.g. the transformation between points C and A ofFIG. 4) or less than 107° C./(ppb/K²) (e.g. the transformation betweenpoints D and A of FIG. 4),

The methods of the present disclosure further extend to implementationof the lower temperature anneal disclosed herein independent of thehigher temperature anneal disclosed herein. A glass article may befabricated and subjected to the lower temperature anneal describedherein without be subjected to the higher temperature anneal describedherein. A glass article may be fabricated, subjected to a standardinitial anneal, and then subjected to the lower temperature annealdescribed herein without be subjected to the higher temperature annealdescribed herein. Implementation of the lower temperature anneal mayinclude heating to the intermediate temperature, cooling to theannealing endpoint temperature at a rate as disclosed hereinabove, andcooling below the annealing endpoint at a rate as disclosed herein. Theintermediate temperature may be as disclosed hereinabove. Theintermediate temperature may be selected to be a temperature below thefictive temperature of the glass article. The intermediate temperaturemay be in the range from 60° C. below the fictive temperature to 10° C.below the fictive temperature, or in the range from 50° C. below thefictive temperature to 20° C. below the fictive temperature, or in therange from 40° C. below the fictive temperature to 20° C. below thefictive temperature. The heating to the intermediate temperature mayexclude exposing the glass article to a temperature greater than thefictive temperature of the glass articles. By selecting the intermediatetemperature to be below the fictive temperature of the glass article andavoiding exposure of the glass article to a temperature above itsfictive temperature, implementation of the lower temperature annealdisclosed herein in the absence of the higher temperature annealdisclosed herein may permit refinement of Tzc without influencing CTEslope or fictive temperature.

The annealing endpoint temperature may be at least 25° C. less than theintermediate temperature, or at least 50° C. less than the intermediatetemperature, or at least 100° C. less than the intermediate temperature.

The rate of cooling from the intermediate temperature to the annealingendpoint temperature may be less than 300° C./hr, or less than 200°C./hr, or less than 100° C./hr, or less than 50° C./hr, or less than 25°C./hr, or less than 10° C./hr, or less than 5° C./hr, or less than 1°C./hr, or less than 0.5° C./hr, or less, or between 0.1° C./hr and 300°C./hr, or between 0.5° C./hr and 100° C./hr, or between 1.0° C./hr and50° C./hr, or between 2.0° C./hr and 25° C./hr, or between 2.0° C./hrand 20° C./hr, or between 2.0° C./hr and 15° C./hr, or between 2.0°C./hr and 10° C./hr. The cooling below the annealing endpointtemperature may include cooling to at least 50° C. below the annealingendpoint temperature, or at least 100° C. below the annealing endpointtemperature, or at least 200° C. below the annealing endpointtemperature.

When implementing the lower temperature anneal in the absence of thehigher temperature anneal, the glass may be transformed from an initialstate having an initial fictive temperature and an initial Tzc to afinished glass article having a final state with a final fictivetemperature and a final Tzc. The final fictive temperature may differfrom the initial fictive temperature by less than 10° C., or less than5° C., or less than 2° C., or less than 1° C., or less than 0.5° C., orless than 0.25° C. The variation in fictive temperature throughout theprocess of transforming the glass from the initial state to the finalstate may be less than 2° C., or less than 1° C., or less than 0.5° C.,or less than 0.25° C. The final Tzc may differ from the initial Tzc byat least 0.25° C., or at least 0.5° C., or at least 1.0° C., or at least2.0° C., or at least 4.0° C., or at least 6.0° C., or at least 8.0° C.,or at least 10.0° C. The final fictive temperature may differ from theinitial fictive temperature by less than 10° C., or less than 5° C., orless than 2° C., or less than 1° C., or less than 0.5° C., or less than0.25° C. and the variation in fictive temperature throughout the processof transforming the glass from the initial state to the final state maybe less than 2° C., or less than 1° C., or less than 0.5° C., or lessthan 0.25° C. and the final Tzc may differ from the initial Tzc by atleast 0.25° C., or at least 0.5° C., or at least 1.0° C., or at least2.0° C., or at least 4.0° C., or at least 6.0° C., or at least 8.0° C.,or at least 10.0° C.

Controlled anneals within the scope of the present disclosure providesilica-titania glasses having paired CTE slope and Tzc values that falloff the correlations dictated by prior art annealing methods. Thetunability in CTE slope and Tzc available from the present methods for agiven composition are unavailable from the prior art methods. In orderto achieve the range of CTE slope and Tzc values from the prior artmethods, it is necessary to vary the composition of the glass. Asindicated hereinabove, variations in the titania content ofsilica-titania glass shift the CTE slope—Tzc correlation to producecomposition-specific correlations that are generally parallel to thecorrelation shown in FIG. 3 for a glass having the composition 7.9 wt %TiO₂-92.0 wt % SiO₂. Compositional variations do afford control over CTEslope and Tzc, but are far less practical to implement than theannealing schedules of the present disclosure. The tunability in CTEslope and Tzc available from the present annealing schedules isequivalent to varying the titania content over a significant range.

Calculations of the titania content needed in a titania-silica glass toachieve representative Tzc values of interest in EUVL lithographyapplications were performed on glasses subjected to the standard initialanneal described hereinabove and subsequently subjected to secondaryannealing according to the prior art or the annealing methods of thepresent disclosure. It may be desirable, for example, to have a glasswith Tzc=25° C. and a CTE slope below 1.30 ppb/K². Silica-titaniaglasses meeting these specifications require a titania content greaterthan or equal to 7.95 wt % when prepared using prior art annealingmethods. With anneals in accordance with the present disclosure,silica-titania glasses having a titania content in the range from 7.45wt % to 8.03 wt % can be transformed to a final state having Tzc=25° C.and a CTE slope below 1.30 ppb/K². Silica-titania glasses having atitania content between 7.45 wt % and less than 7.95 wt % can thus betuned with the present method, but not with the prior art method, to afinal state having Tzc=25° C. and a CTE slope below 1.30 ppb/K².

Silica-titania glasses having Tzc=35° C. and CTE slope below 1.30 ppb/K²require a titania content greater than or equal to 8.13 wt % whenprepared using prior art annealing methods. With anneals in accordancewith the present disclosure, silica-titania glasses having a titaniacontent in the range from 7.62 wt % to 8.20 wt % can be transformed to afinal state having Tzc=35° C. and a CTE slope below 1.30 ppb/K².Silica-titania glasses having a titania content between 7.62 wt % andless than 8.13 wt % can thus be tuned with the present method, but notwith the prior art method, to a final state having Tzc=35° C. and a CTEslope below 1.30 ppb/K².

Silica-titania glasses having Tzc=25° C. and CTE slope below 1.25 ppb/K²require a titania content greater than or equal to 8.07 wt % whenprepared using prior art annealing methods. With anneals in accordancewith the present disclosure, silica-titania glasses having a titaniacontent in the range from 7.56 wt % to 8.14 wt % can be transformed to afinal state having Tzc=25° C. and a CTE slope below 1.25 ppb/K².Silica-titania glasses having a titania content between 7.56 wt % andless than 8.07 wt % can thus be tuned with the present method, but notwith the prior art method, to a final state having Tzc=25° C. and a CTEslope below 1.25 ppb/K².

Silica-titania glasses having Tzc=35° C. and CTE slope below 1.25 ppb/K²require a titania content greater than or equal to 8.23 wt % whenprepared using prior art annealing methods. With anneals in accordancewith the present disclosure, silica-titania glasses having a titaniacontent in the range from 7.72 wt % to 8.30 wt % can be transformed to afinal state having Tzc=35° C. and a CTE slope below 1.25 ppb/K².Silica-titania glasses having a titania content between 7.72 wt % andless than 8.23 wt % can thus be tuned with the present method, but notwith the prior art method, to a final state having Tzc=35° C. and a CTEslope below 1.25 ppb/K².

The results also indicate that silica-titania glasses having a titaniacontent in the range from 7.72 wt % to less than 8.03 wt % can be tunedwith the methods of the present disclosure to any of the fourillustrative conditions set forth above (1. Tzc=25° C. and CTE slopeless than 1.30 ppb/K²; 2. Tzc=35° C. and CTE slope less than 1.30ppb/K²; 3. Tzc=25° C. and CTE slope less than 1.25 ppb/K²; 4. Tzc=35° C.and CTE slope less than 1.25 ppb/K²). Any of the four conditions can beachieved within the composition window without a need to modify theconditions of the glass forming process. Post-formation annealingtreatments in accordance with the present disclosure provide thetunability necessary within the composition window to achieve finalstates meeting any of the four illustrative conditions.

The present annealing treatments provide tunability of Tzc and CTE slopeover wide ranges. In one embodiment, the annealing conditions can beadjusted to provide a silica-titania glass having a titania contentbetween 7.45 wt % and 8.39 wt %, where the glass has Tzc in the rangefrom 15° C. to 45° C. and a CTE slope at 20° C. below 1.30 ppb/K². Theglass may also include OH. The concentration of OH in the glass may bein the range from 700 ppm to 1000 ppm.

In another embodiment, the annealing conditions can be adjusted toprovide a silica-titania glass having a titania content between 7.45 wt% and 8.31 wt %, where the glass has Tzc in the range from 25° C. to 45°C. and a CTE slope at 20° C. below 1.30 ppb/K². The glass may alsoinclude OH. The concentration of OH in the glass may be in the rangefrom 700 ppm to 1000 ppm. The annealing conditions may also be adjustedto provide a silica-titania glass having Tzc in the range from 25° C. to45° C. and a CTE slope at 20° C. below 1.30 ppb/K², where the titaniacontent is between 7.45 wt % and [7.95 wt %+(Tzc−25° C.)*(0.018 wt %/°C.)]. The glass may also include OH. The concentration of OH in theglass may be in the range from 700 ppm to 1000 ppm.

In still another embodiment, the annealing conditions can be adjusted toprovide a silica-titania glass having a titania content between 7.56 wt% and less than 8.39 wt %, where the glass has Tzc in the range from 25°C. to 45° C. and a CTE slope at 20° C. below 1.25 ppb/K². The glass mayalso include OH. The concentration of OH in the glass may be in therange from 700 ppm to 1000 ppm. The annealing conditions may also beadjusted to provide a silica-titania glass having Tzc in the range from25° C. to 45° C. and a CTE slope at 20° C. below 1.25 ppb/K², where thetitania content is between 7.56 wt % and [8.07 wt %+(Tzc−25° C.)*(0.016wt %/° C.)]. The glass may also include OH. The concentration of OH inthe glass may be in the range from 700 ppm to 1000 ppm.

In yet another embodiment, the annealing conditions can be adjusted toprovide a silica-titania glass having a titania content between 7.62 wt% and 8.13 wt %, where the glass has Tzc in the range from 25° C. to 35°C. and a CTE slope at 20° C. below 1.30 ppb/K². The glass may alsoinclude OH. The concentration of OH in the glass may be in the rangefrom 700 ppm to 1000 ppm. The annealing conditions may also be adjustedto provide a silica-titania glass having Tzc in the range from 25° C. to35° C. and a CTE slope at 20° C. below 1.30 ppb/K², where the titaniacontent is between 7.62 wt % and [7.95 wt %+(Tzc−25° C.)*(0.018 wt %/°C.)]. The glass may also include OH. The concentration of OH in theglass may be in the range from 700 ppm to 1000 ppm.

In a further embodiment, the annealing conditions can be adjusted toprovide a silica-titania glass having a titania content between 7.72 wt% and 8.23 wt %, where the glass has Tzc in the range from 25° C. to 35°C. and a CTE slope at 20° C. below 1.30 ppb/K². The glass may alsoinclude OH. The concentration of OH in the glass may be in the rangefrom 700 ppm to 1000 ppm. The annealing conditions may also be adjustedto provide a silica-titania glass having Tzc in the range from 25° C. to35° C. and a CTE slope at 20° C. below 1.25 ppb/K², where the titaniacontent is between 7.72 wt % and [8.07 wt %+(Tzc−25° C.)*(0.016 wt %/°C.)]. The glass may also include OH. The concentration of OH in theglass may be in the range from 700 ppm to 1000 ppm.

The tunability extends as well as to many other final state combinationsof Tzc and CTE slope not explicitly identified, but nonetheless readilyappreciated by those of skill in the art. It is also a feature of theannealing treatments disclosed herein that they achieve the resultswhile keeping the run length approximately constant. This isadvantageous for planning at the glass production plant.

Example 1

FIG. 6 illustrates representative annealing schedules in accordance withthe present disclosure. Six annealing schedules are depicted. Eachannealing schedule includes heating to an elevated temperature of 950°C. and holding at 950° C. for several hours. Annealing schedules 1-3include a common rate of cooling from 950° C. to an intermediatetemperature of 825° C. and differ in the rate of cooling from 825° C. toan annealing endpoint temperature of 700° C. Annealing schedules 4-6include a common rate of cooling from 950° C. to an intermediatetemperature of 825° C. and differ in the rate of cooling from 825° C. toan annealing endpoint temperature of 700° C. The rate of cooling between950° C. and 825° C. differs for annealing schedules 1-3 and annealingschedules 4-6. The cooling rate below 700° C. to room temperature is thesame for annealing schedules 1-6.

Although not explicitly shown, several additional annealing schedules ofthe type shown in FIG. 6 were devised with the same initial heating andholding conditions, the same elevated temperature (950° C.), the sameintermediate temperature (825° C.), the same annealing endpointtemperature (700° C.), and the same cooling rate below the annealingendpoint temperature to room temperature. The additional annealingschedules differed in the rates of cooling between 950° C. and 825° C.and/or between 825° C. and 700° C.

Calculated values of CTE slope at 20° C. and Tzc for a silica-titaniaglass with the composition 7.9 wt % TiO₂-92.0 wt % SiO₂ are presented inFIG. 7. The calculations were based on anneals of the type shown in FIG.6. FIG. 7 also reproduces as trace 16 the data shown in FIG. 3. Thecalculated data segregate into a series of approximately linear traces,where the data points of each trace are connected by line segments asshown. The temperature schedule for each set of connected data pointsincluded a different rate of cooling between the elevated temperature(950° C.) and intermediate temperature (825° C.) of the anneal and acommon rate of cooling between the intermediate temperature (825° C.)and annealing endpoint temperature (700° C.). Data points from differenttraces that align vertically were obtained from glass samples subjectedto temperature schedules that included a common rate of cooling betweenthe elevated temperature (950° C.) and intermediate temperature (825°C.) of the anneal and a different rate of cooling between theintermediate temperature (825° C.) and annealing endpoint temperature(700° C.).

The data shown in FIG. 7 demonstrate an ability to independently controlTzc and CTE slope of silica-titania glass with a fixed composition. Fora particular CTE slope, it becomes possible with the present methods toobtain a range of Tzc values by varying the rate of cooling from theintermediate temperature to the annealing endpoint temperature. If aparticular application, for example, requires a CTE slope of 1.25 ppb/K²for a silica-titania glass of a given composition, it becomes possibleto tune Tzc over a temperature range of ˜20° C. (e.g. from ˜12° C. to˜32° C.) by controlling the cooling rate from the intermediatetemperature to the annealing endpoint temperature. Using the annealingschedule of the prior art, in contrast, provides only a glass with Tzcof ˜15° C. if a CTE slope of 1.25 ppb/K² is desired. Similarly, for aparticular Tzc, it becomes possible with the present methods to obtain arange of CTE slope values by varying the rate of cooling between theelevated temperature and intermediate temperature and the rate ofcooling between the intermediate temperature and the annealing endpointtemperature.

Glass samples subjected to annealing schedules 1-3 of FIG. 6 have acommon cooling rate between the elevated temperature (950° C.) and theintermediate temperature (825° C.) and different cooling rates betweenthe intermediate temperature (825° C.) and the annealing endpointtemperature (700° C.). Glass samples subjected to annealing schedules1-3 of FIG. 6 thus have a common CTE slope and differing Tzc values.Data points for these samples align vertically in FIG. 7.

While not wishing to be bound by theory, it is believed that cooling inthe temperature window of the first controlled anneal (between theelevated temperature and intermediate temperature) influences thefictive temperature of the glass article and that variations in thefictive temperature provide control over the CTE slope of the glassarticle. Tzc is also influenced in the temperature window of the firstcontrolled anneal, but essentially only in a manner that correlates withthe variation in CTE slope (consistent with the expected effects of theprior art anneal described hereinabove). It is also believed herein thatcooling in the temperature window of the second controlled anneal(between the intermediate temperature and the annealing endpointtemperature) further influences the internal structure or physical stateof the glass article. An underlying assumption associated with the priorart secondary annealing process is that the state of a silica-titaniaglass, including CTE slope and Tzc, are fixed upon cooling to atemperature of ˜800° C. The presumption of the prior art secondaryannealing process is that cooling in the temperature regime below ˜800°C. has no substantive effect on the structure or properties of asilica-titania glass. The present disclosure, in contrast, demonstratesthat cooling in the temperature regime below ˜800° C. continues toinfluence the properties of silica-titania glasses. Cooling, forexample, in the temperature range from ˜800° C. to ˜700° C. has beenshown herein to influence Tzc with little or no influence on CTE slope.Although variations in Tzc occur in the prior art annealing process,they occur in conjunction with variations in CTE slope to providecorrelated values of CTE slope and Tzc. Control of Tzc independent ofCTE slope is a feature provided by the methods of the present disclosurethat is unavailable from the methods of the prior art.

While not wishing to be bound by theory, it is believed that cooling inthe lower temperature range associated with the second controlled annealof the present disclosure influences a secondary fictive temperature ofsilica-titania glass. Like fictive temperature, it is believed that thesecondary fictive temperature is an indicator of the internal structure,distribution of strains, or inhomogeneities of the glass. It isbelieved, however, that the time or length scales of the phenomenaassociated with the fictive temperature and secondary fictivetemperature differ. It is further believed that the structural orrelaxational phenomena associated with the fictive temperature andsecondary fictive temperature are temperature dependent, but that thequenching temperature of the phenomena associated with the fictivetemperature is higher than the quenching temperature of the phenomenaassociated with the secondary fictive temperature.

It is proposed herein that the structural and relaxational phenomenathat establish the fictive temperature in silica-titania glass can beinfluenced during an annealing process through the selection of coolingrate in a temperature window above ˜800° C. Below ˜800° C., it isbelieved that the phenomena that establish the fictive temperature havequenched and become temperature insensitive. It is further proposedherein that while the structural and relaxational phenomena associatedwith the secondary fictive temperature may be influenced by the coolingrate above 800° C., they continue to be influenced by the cooling rateat temperatures below 800° C. The phenomena associated with thesecondary fictive temperature may be influenced down to temperatures aslow as about 650° C. It is believed that the phenomena that establishfictive temperature have primary control over CTE slope, while thephenomena that establish secondary fictive temperature have primarycontrol over Tcz. Since the different phenomena that establish fictiveand secondary temperature quench at different temperatures, it becomespossible to achieve independent control over CTE slope and Tcz asdemonstrated herein.

Example 2

FIG. 8 shows alternative annealing schedules that permit independentcontrol of Tzc and CTE slope. Six representative annealing schedules areshown. Each annealing schedule includes heating to an elevatedtemperature of 950° C. and holding at 950° C. for several hours.Annealing schedules 1-3 include a common rate of cooling from 950° C. todifferent intermediate temperatures (˜860° C., ˜825° C., and ˜780° C.)followed by cooling at a common faster rate to room temperature.Annealing schedules 4-6 include a common rate of cooling (different fromthe rate of cooling used for annealing schedules 1-3) from 950° C. todifferent intermediate temperatures (˜855° C., ˜815° C., and ˜770° C.)followed by cooling at a common faster rate (the same faster rate asused in annealing schedules 1-3) to room temperature.

The common rate of cooling from the elevated temperature for annealingschedules 1-3 shown in FIG. 8 is expected to establish a common fictivetemperature and a common CTE slope. Differences in the intermediatetemperature are expected to lead to differences in Tzc and thepostulated secondary fictive temperature described hereinabove. Similarconclusions hold for annealing schedules 4-6 shown in FIG. 8. Thedifference in the cooling rate from 950° C. for annealing schedules 1-3relative to annealing schedules 4-6 in FIG. 8 is expected to lead todifferent CTE slopes.

To verify the trends expected for the annealing schedules shown in FIG.8, tests were performed on a series of twelve glass samples extractedfrom a common boule of ULE® glass. The boule was not compositionallyuniform and included regions exhibiting small variations in composition.The twelve samples were selected as two sets of six samples extractedfrom regions of the boule that differed slightly in composition. The setof six samples referred to as “Series 1” had a composition with 7.2 wt %TiO₂ and 92.7 wt % SiO₂ and the set of six samples referred to as“Series 2” had a composition with 7.5 wt % TiO₂ and 92.4 wt % SiO₂. OHcontent was about 850 ppm by weight in all samples. Each of the sixSeries 1 glass samples had an initial Tzc of 13° C. and an initial CTEslope of 1.60 ppb/K² and each of the six Series 2 glass samples had aninitial Tzc of 24° C. and an initial CTE slope of 1.60 ppb/K².

The annealing schedules employed are shown in FIG. 9. Each annealingschedule included heating to an elevated temperature of 950° C., holdingat 950° C. for several hours, cooling at a common rate to a particularintermediate temperature, and cooling at a common faster rate to roomtemperature. The intermediate temperature differed for the six annealingschedules. Six intermediate temperatures, ranging from 875° C. to 750°C., were employed. The six annealing schedules are labelled with anidentifying number 1-6 in FIG. 9. Each sample within each series of sixsamples was subjected to a different one of the six annealing schedules.After completion of the annealing process, CTE slope at 20° C. and Tzcwere measured for each of the samples. The fictive temperature (TO ofeach sample was also calculated using a well-established model.

FIG. 10 shows Tzc and CTE slope for each of the twelve samples. TheSeries 1 data points correspond to the set of six samples having aninitial Tzc of 13° C. and an initial CTE slope of 1.60 ppb/K², and theSeries 2 data points correspond to the set of six samples having aninitial Tzc of 24° C. and an initial CTE slope of 1.60 ppb/K². Theannealing schedule associated with each data point is labeled accordingto the identifying number presented in FIG. 9. The data in FIG. 10demonstrate that Tzc can be varied within each set of samples over arange of ˜13° C. while maintaining an approximately constant CTE slope.

The most pronounced variability in CTE slope was observed for annealingschedule 1. The origin of the variability is believed to be due to asmall variation of fictive temperature (TO that accompanied annealingschedule 1 Annealing schedule 1 had the highest intermediate temperature(875° C.) and was subjected to rapid cooling after a shorter coolingtime at the slower cooling rate. It is believed that the fictivetemperature of the glass composition was not fully established by 875°C. and that samples subjected to annealing schedule 1 accordingly hadhigher fictive temperatures. As the intermediate temperature of theannealing schedule was decreased, it is believed that the relaxationalprocesses that establish fictive temperature fully quenched and that thefictive temperature stabilized accordingly. The correlation between CTEslope and fictive temperature shown in FIG. 11 is consistent with theseexpectations. The highest fictive temperature and largest CTE slope wasobserved for annealing schedule 1. Fictive temperature and CTE slopewere observed to stabilize for annealing schedules 3-6. The range ofvariation of CTE slope over the set of six annealing schedules wasobserved to be ˜0.05 ppb/K². Substantially smaller variations in CTEslope are expected for annealing schedules of the type shown in FIG. 6.For comparison purposes, in order to achieve the ˜13° C. tuning rangefor Tzc observed for annealing schedules 1-6, the variation in CTE slopewould be ˜0.13 ppb/K² for conventional annealing schedules of the typeshown in FIG. 2.

Unless otherwise expressly stated, it is in no way intended that anymethod set forth herein be construed as requiring that its steps beperformed in a specific order. Accordingly, where a method claim doesnot actually recite an order to be followed by its steps or it is nototherwise specifically stated in the claims or descriptions that thesteps are to be limited to a specific order, it is no way intended thatany particular order be inferred.

It will be apparent to those skilled in the art that variousmodifications and variations can be made without departing from thespirit or scope of the invention. Since modifications combinations,sub-combinations and variations of the disclosed embodimentsincorporating the spirit and substance of the invention may occur topersons skilled in the art, the invention should be construed to includeeverything within the scope of the appended claims and theirequivalents.

What is claimed is:
 1. A method of annealing glass comprising: providinga silica-titania glass article, said silica-titania glass article havinga first Tzc and a first CTE slope at 20° C.; heating said glass articleto a first temperature, said first temperature being higher than 850°C.; cooling said glass article at a first rate from said firsttemperature to a second temperature, said second temperature being inthe range from 750° C. to 875° C.; cooling said glass article at asecond rate from said second temperature to a third temperature, saidsecond rate exceeding said first rate, said third temperature being inthe range from 650° C. to 775° C.; and cooling said glass article at athird rate below said third temperature, said third rate exceeding saidsecond rate, said cooling at said third rate producing a finishedsilica-titania glass article, said finished silica-titania glass articlehaving a second Tzc and a second CTE slope at 20° C., said second Tzcdiffering from said first Tzc.
 2. The method of claim 1, wherein saidfirst temperature is in the range from 900° C. and 950° C., said secondtemperature is in the range from 800° C. to 850° C., and said thirdtemperature is in the range from 700° C. to 750° C.
 3. The method ofclaim 1, wherein said first cooling rate is in the range from 0.01°C./hour to 5.0° C./hour and said second cooling rate is in the rangefrom 0.1° C./hour to 300° C./hour.
 4. The method of claim 1, whereinsaid first cooling rate is in the range from 0.10° C./hour to 5.0°C./hour and said second cooling rate is in the range from 0.5° C./hourto 100° C./hour.
 5. The method of claim 1, wherein said silica-titaniaglass article has a titania content in the range from 7 wt % to 12 wt %.6. The method of claim 1, wherein said second Tzc differs from saidfirst Tzc by at least 4° C. and said second CTE slope at 20° C. differsfrom said first CTE slope at 20° C. by less than 0.05 ppb/K².
 7. Amethod of annealing glass comprising: providing a silica-titania glassarticle, said silica-titania glass article having a first fictivetemperature and a first Tzc; heating said glass article to a firsttemperature, said first temperature being in the range from 60° C. belowsaid first fictive temperature to 10° C. below said first fictivetemperature, said heating excluding exposing said glass article to atemperature greater than said first fictive temperature; cooling saidglass article at a first rate from said first temperature to a secondtemperature, said second temperature being at least 25° C. less thansaid first temperature; cooling said glass article at a second rate to athird temperature, said third temperature being at least 50° C. lessthan said second temperature, said second rate exceeding said firstrate, said cooling producing a finished silica-titania glass article,said finished silica-titania glass article having a second fictivetemperature and a second Tzc, said second fictive temperature differingfrom said first fictive temperature by less than 10° C., said second Tzcdiffering from said first Tzc by at least 0.5° C.
 8. The method of claim7, wherein said first temperature is in the range from 40° C. below saidfirst fictive temperature to 20° C. below said first fictivetemperature.
 9. The method of claim 7, wherein said second temperatureis at least 50° C. less than said first temperature.
 10. The method ofclaim 7, wherein said first cooling rate is in the range from 0.5°C./hour to 100° C./hour.
 11. The method of claim 7, wherein said secondfictive temperature differs from said first fictive temperature by lessthan 5° C. and said second Tzc differs from said first Tzc by at least3° C.
 12. A silica-titania glass having a titania content between 7.45wt % and 8.39 wt %, said glass having Tzc in the range from 15° C. to45° C. and a CTE slope at 20° C. below 1.30 ppb/K².
 13. Thesilica-titania glass of claim 12, wherein said Tzc is in the range from25° C. to 45° C. and said titania content is between 7.45 wt % and (7.95wt %+(Tzc−25° C.)*(0.018 wt %/° C.).
 14. The silica-titania glass ofclaim 13, wherein said glass includes an OH concentration in the rangefrom 700 ppm to 1000 ppm.
 15. The silica-titania glass of claim 12,wherein said Tzc is in the range from 25° C. to 45° C., said CTE slopeat 20° C. is below 1.25 ppb/K², and said titania content is between 7.56wt % and [8.07 wt %+(Tzc−25° C.)*(0.016 wt %/° C.)].
 16. Thesilica-titania glass of claim 15, wherein said glass includes an OHconcentration in the range from 700 ppm to 1000 ppm.
 17. Thesilica-titania glass of claim 12, wherein said Tzc is in the range from25° C. to 35° C. and said titania content is between 7.62 wt % and [7.95wt %+(Tzc−25° C.)*(0.018 wt %/° C.)].
 18. The silica-titania glass ofclaim 17, wherein said glass includes an OH concentration in the rangefrom 700 ppm to 1000 ppm.
 19. The silica-titania glass of claim 12,wherein said Tzc is in the range from 25° C. to 35° C., said CTE slopeat 20° C. is below 1.25 ppb/K², and said titania content is between 7.72wt % and [8.07 wt %+(Tzc−25° C.)*(0.016 wt %/° C.).].
 20. Thesilica-titania glass of claim 19, wherein said glass includes an OHconcentration in the range from 700 ppm to 1000 ppm.